Place chicken in a large bowl and season with salt and pepper. Toss to coat.
Heat 2 tablespoons vegetable oil in a large pan and over medium. Add chicken to the pan and sauté until browned and cooked through, about 5 to 7 minutes. Transfer chicken to a medium bowl.
Heat 2 more tablespoons of oil in the pan over medium. Add in carrot, onion, bell pepper, zucchini, and lemongrass and cook until just softened, about 5 minutes.
Stir in red curry paste and fish sauce. Lower heat and cook for five minutes, stirring occasionally.
Add coconut milk and chicken broth. Bring to a gentle boil over medium heat and cook for 10 minutes, then reduce heat to low. Add chicken, stir all ingredients well and cook until heated through, about three minutes.
To serve, spoon chicken curry over brown rice and garnish with cilantro, green onions, cashews, and a squeeze of lime.